Driven well chlorination

This is a basic question that was probably already posted (or not because not found), but here I go.

I have a 2" driven well, PVC pipes, around 20 feet deep. I want to pour down chlorine to do a shock chlorination. But I seem to be missing something here. The pipe heads out about 1 feet overground. So I remove the cap and pour down the chlorine solution. The problem is that it fills up with less than a few cup and does not seem to go down. I guess I have a pitless adapter and it does not get pass through it and there is nothing I can do there. After many hours the chlorine will have gone "somewhere" but it never smells chlorine at the faucets. I'm even beginning to think that I am doing more harm than good with the chlorine mixture sitting there for all those hours.

By principle, when I do not find a solution on the Internet then I should not be having a problem because it does not exist.... So can somebody point me out in the right direction.

There would be a pitless adapter, at least six feet down (below frost level) between the screen pipe and the pipe that goes in the house. The check valve is just between the pump and the pipe in the house (this I can confirm). I do not see why there would be another chech valve at the junction of the two pipes. I am not able to look down the pvc pipe to confirm the type of adapter...

There has to be a check valve betweem the pitless adapter and the well point otherwise the chlorine would go down!

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If it is the case, does not seem a good idea since I already have a check valve at the pump. Also, the chlorine manage to get pass (where?), but after many hours (I did not check exactly how many but less than a day...) which I find strange. Not practical and I wonder if such long contact with the pipes (PVC) and adapter can harm.

I guess I will try to locate the person who drove and installed the pipes and get in touch with him.